Unit 3

Test on Tuesday, January 31st (C-day - 70 minute class)

The following problems are homework for the month of January. The dates shown are when the homework is DUE.

• Jan 5 - page 133 #1 to #38 (odd; do all for extra credit)
• Jan 6 - page 135 #1 to #38 (odd; do all for extra credit)
• Jan 9 - page 137 (class exercises) #1 to #16
• Jan 10 - page 138 (written exercises) #1 to #42 (odd; do all for extra credit)
• Jan 10 - page 141 (written exercises) #1 to #39 (odd; do all for extra credit)
• Jan 11 - page 142 (self-test A) #1 to #16 (odd; do all for extra credit)
• extra credit - page 148 #1 to #16
• extra credit - page 150 #1 to #10
• Jan 12 - page 283 (class exercises) #1 to #23
• Jan 13 - page 283 (written exercises) #1 to #12
• Jan 16 - page 284 (written exercises) #13 to #30
• Jan 18 - page 284 (written exercises) #31 to #42
• Jan 20 - page 284 (written exercises) #43 to #48
• Jan 24 - page 286 (written exercises) #1 to #18 (time given in class)
• Jan 24 - page 286 (written exercises) #19 to #30 (time given in class)
• Jan 24 - page 286 (written exercises) #31 to #36 (time given in class)
• extra credit - page 288-289 (problems) #1 to #14
• Jan 25 - page 290 (self test A) #1 to #10
• Jan 25 - page 290 (self test A) #11 to #16
• Jan 26 - page 295 (written exercises) #1 to #9
• Jan 26 - page 295 (written exercises) #10 to #18
• Jan 27 - page 296 (written exercises "B") #25 to #52 (odd; do all for extra credit)
• Jan 30 - page 299 (written exercises) #1 to #26
• extra credit - page 302-303 #1 to #11

Linear Equation Tool

Click on the image below to activate the linear equation tool. It is useful because it allows you to try different strategies and "undo" the steps.

Make sure that you can solve all 20 problems. The red circles are different problems with (1) being the easiest and higher numbers more challenging.

**__West Texas A&M University -Solving Linear Equations Tutorial__**

West Texas A&M University -Solving Linear Inequalities Tutorial

Many examples with problems fully solved:

1. Solving Equations, Example 1: x + a = b
2. Solving Equations, Example 2: x - a = b
3. Solving Equations, Example 3: x + a = -b
4. Solving Equations, Example 4: x - a = -b
5. Solving Equations, Example 5: ax + b = c
6. Solving Equations, Example 6: ax - b = c
7. Solving Equations, Example 7: ax + b = -c
8. Solving Equations, Example 8: -ax + b = c
9. Solving Equations, Example 9: -ax - b = c
10. Solving Equations, Example 10: -ax + b = -c
11. Solving Equations, Example 11: -ax - b = -c
12. Solving Equations, Example 12: ax + b = cx + d
13. Solving Equations, Example 13: ax - b = cx + d
14. Solving Equations, Example 14: ax + b = cx - d
15. Solving Equations, Example 15: ax - b = cx - d
16. Solving Equations, Example 16: ax + b = -cx + d
17. Solving Equations, Example 17: ax - b = -cx + d
18. Solving Equations, Example 18: ax + b = -cx - d
19. Solving Equations, Example 19: ax - b = -cx - d
20. Solving Equations, Example 20: -ax + b = cx + d
21. Solving Equations, Example 21: -ax - b = cx + d
22. Solving Equations, Example 22: -ax + b = -cx + d
23. Solving Equations, Example 23: -ax - b = -cx + d
24. Solving Equations, Example 24: -ax + b = -cx + d
25. Solving Equations, Example 25: -ax + b = -cx - d
26. Solving Equations, Example 26: -ax - b = cx - d
27. Solving Equations, Example 27: -ax - b = -cx - d

Solving Linear Equations (thanks for Carmen for contributing this video)

Solving Linear Equations (Patrick JMT)

More examples of Solving Linear Equations (Patrick JMT)

Still More examples of Solving Linear Equations (Patrick JMT)

Checking the Solution of a Linear Equation (Patrick JMT)

Solving Linear Equations - Part 2 (Khan Academy)

Solving Linear Equations - Part 3 (Khan Academy)

Solving Linear Equations - Part 4 (Khan Academy)

Commutative property of addition

Associative property of addition

Commutative property of multiplication

Associative property of multiplication

Identity property of addition

Identity property of multiplication

Distributive property

The distributive property has the form n(a + b + c) and results in n(a) + n(b) + n(c).

It is also possible to distribute a negative multiplier, such as -n(a + b + c), which results in -n(a) + -n(b) + -n(c)

Two similiar examples:

• 35 + 3(2.50 + 1.50 + 1.00) --> 35 + 3(2.50) + 3(1.50) + 3(1.00) --> 35 + 15 = 50

• 35 - 3(2.50 + 1.50 + 1.00) --> 35 - [ 3(2.50) + 3(1.50) + 3(1.00) ] --> 35 - 15 = 20

It is important notice that when the multiplier is negative, more care must be taken with the distribution. The negative 3 must be multipled by each term inside of the parenthesis.

Two more complicated examples:

• 10 + 3(5 - 3 - 2) --> 10 + 3(5) + 3(-3) + 3(-2) --> 10 + 15 + (-9) + (-6) = 10

• 10 + -3(5 - 3 - 2) --> 10 + -3(5) + -3(-3) + -3(-2) --> 10 + (-15) + 9 + 6 = 0

Rules for solving equations